
#1




Principal Component Analysis
I am having trouble understanding Principal Component Analysis, which I understand is now part of MAS !!. Would someone kindly share a simple numerical example in Excel or R so I can follow the calculation, and also explain what one then does with the numerical result?
Thank you, Jerry
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Thanks, Jerry 
#3




It's probably easier to think about it geometrically.
PCA is a dimension reduction technique. Suppose that you have a data set with three variables. Your data looks like (X+noise1, 3X+noise2, X+noise3) where X is some random variable and noisei (i=1,2,3) is, well, noise (and small compared to X on average. The data set looks like a thickened blob lying along the subspace spanned by (1, 3, 1). PCA asks the question: if I had to approximate this dataset with a single direction (one dimensional subspace), which direction should I use. The answer has several interpretations: which direction captures the most variation I the dataset? Once that direction is known, we project the dataset onto it, compute the orthogonal complement and repeat. This yields a sequence of vectors which we use (in order) to form a nested sequence of vector spaces (of dimensions, 1, 2, 3, … ) that are in some sense best approximations to our data. That should get you started.
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